# Graph of a Quadratic Functions

- Author:
- Almar Alvarado, cwinske

- Topic:
- Functions, Quadratic Functions

*Good morning class!***Welcome to another day filled with enjoyable activities and learning!**

## What do these pictures have the same in common?

## DEFINITION OF TERMS

**domain of quadratic function**- the set of all possible values of x. Thus, the domain is the set of all real numbers.

**range of quadratic functions**– consists of all y greater than or equal to the y coordinate of the vertex if the parabola opens upward.

**intercepts or zeroes of quadratic functions**– the values of x when y equals 0. The real zeros are the x-intercepts of the function’s graph.

**axis of symmetry / line of symmetry**– the vertical line through the vertex that divides the parabola into two equal parts.

**vertex**– the turning point of the parabola or the lowest or highest point of the parabola. If the quadratic function is expressed in the standard form y = a(x-h)2+ k, the vertex is the point of (h,k).

**direction of the opening of the parabola**– can be determined from the value of a in f(x) = ax

^{2}+bx + c. If a>0, the parabola opens upward; if a<0, the parabola opens downward.

**maximum value**– the maximum value of f(x) = ax

^{2}+bx + c where a< 0, is the y coordinate of the vertex.

**minimum value**– the minimum value of f(x) = ax

^{2}+bx + c where a> 0, is the y coordinate of the vertex.

**parabola**– the graph of quadratic function

**quadratic function**– a second- degree function of the form f(x) = ax

^{2}+bx + c, where a, b, and c are real numbers and a≠0. This is a function which describes a polynomial

**Try to answer the following activity, observe the behavior of the graph of a quadratic function as you changes the values of a, b, and c. Write your observation below.**

## Watch this video and learn how to graph a quadratic equation.

## Answer the following activity. (just choose 3 items in part 1 and other 3 in part 2.

*THANK YOU FOR TODAY!*